1. Field of the Invention
The present invention relates to an electronic circuit for treating an analog signal. In particular, the present invention relates to a reference current generating circuit that generates a stable reference current.
2. Description of Related Art
A reference current generated by a reference current generating circuit is supplied to another electronic circuit such as an operational amplifier and used as an operating point current that is a basis of a circuit operation. It is desirable that an operation and characteristics of the electronic circuit to which the reference current is supplied are stable with respect to variable factors such as a junction temperature. This requires the reference current generated by the reference current generating circuit to be also stable with respect to variable factors such as the junction temperature.
A reference current generating circuit is disclosed, for example, in Japanese Patent Publication JP-2001-142552. FIG. 1 shows a configuration of the reference current generating circuit X1. The reference current generating circuit X1 is provided with: N-channel MOS transistors M11 to M12, M16 to M17; P-channel MOS transistors M13 to M15; resistors R11 to R13; a PN junction diode D11; an output node CM1; and power supply terminals VDD and GND. All the MOS transistors are enhancement (normally off) type. Although description of a connection to a back gate of the MOS transistor is omitted in FIG. 1, the back gate may be connected to a source of the MOS transistor. Alternatively, a back gate of the N-channel MOS transistor may be connected to the power supply terminal GND, and a back gate of the P-channel MOS transistor may be connected to the power supply terminal VDD.
An operation of the reference current generating circuit X1 will be described below. In the reference current generating circuit X1, the N-channel MOS transistors M11 and M12 constitute a Widlar current mirror circuit. The P-channel MOS transistors M13 to M15 constitute a typical linear current mirror circuit whose input side is the transistor M14. The N-channel MOS transistors M16 and M17 also constitute a typical linear current mirror circuit whose input side is the transistor M16. The Widlar current mirror circuit has nonlinearity characteristics. An input and an output of the Widlar current mirror circuit are connected to the linear current mirror circuit, and the circuits as a whole constitutes a self-feedback circuit. A current flowing in the circuits as a whole is stabilized and converged to either zero or a specific value that is determined by respective circuit constants of the both current mirror circuits with which respective input/output current values match with each other.
Let us calculate the non-zero specific current values I1 to I4. Let Wx and Lx respectively denote a gate width and a gate length of a MOS transistor Mx (x is an element number). For simplifying of circuit analysis, characteristics such as electron mobility, hole mobility and a gate capacitance per unit area are the same between MOS transistors of the same polarity among the transistors M11 to M17. In the transistor Mx, let I0x denote a drain current in a case where a gate-source voltage is equal to a threshold voltage, and let Vt denote a thermal voltage (Vt=k×T/q: k is the Boltzmann constant, T is an absolute temperature, and q is unit charge). According to Japanese Patent Publication JP-2001-142552, the N-channel MOS transistors M11 and M12 operate in a sub-threshold region. Therefore, when a drain current and a gate-source voltage of the transistor M11 are expressed by I1 and V1, respectively, and a drain current and a gate-source voltage of the transistor M12 are expressed by I2 and V2, respectively, the following equations (1) to (3) can be obtained.
                              I          ⁢                                          ⁢          1                =                  I          ⁢                                          ⁢                      011            ·                                          W                ⁢                                                                  ⁢                11                                            L                ⁢                                                                  ⁢                11                                      ·                          exp              ⁡                              (                                                      V                    ⁢                                                                                  ⁢                    1                                    Vt                                )                                                                        (        1        )                                          I          ⁢                                          ⁢          2                =                  I          ⁢                                          ⁢                      012            ·                                          W                ⁢                                                                  ⁢                12                                            L                ⁢                                                                  ⁢                12                                      ·                          exp              ⁡                              (                                                      V                    ⁢                                                                                  ⁢                    2                                    Vt                                )                                                                        (        2        )                                          V          ⁢                                          ⁢          1                =                              V            ⁢                                                  ⁢            2                    +                      I            ⁢                                                  ⁢                          2              ·              R                        ⁢                                                  ⁢            11                                              (        3        )            
By substituting the equations (1) and (2) into the equation (3), we obtain the following equation (4).
                              I          ⁢                                          ⁢          2                =                ⁢                                            1                              R                ⁢                                                                  ⁢                11                                      ·                          (                                                V                  ⁢                                                                          ⁢                  1                                -                                  V                  ⁢                                                                          ⁢                  2                                            )                                =                                                                      1                                      R                    ⁢                                                                                  ⁢                    11                                                  ·                                  {                                                            Vt                      ·                                              ln                        (                                                                              I                            ⁢                                                                                                                  ⁢                            1                                                                                I                            ⁢                                                                                                                  ⁢                                                          011                              ·                                                                                                W                                  ⁢                                                                                                                                          ⁢                                  11                                                                                                  L                                  ⁢                                                                                                                                          ⁢                                  11                                                                                                                                                                    )                                                              -                                          Vt                      ·                                              ln                        (                                                                              I                            ⁢                                                                                                                  ⁢                            2                                                                                I                            ⁢                                                                                                                  ⁢                                                          012                              ·                                                                                                W                                  ⁢                                                                                                                                          ⁢                                  12                                                                                                  L                                  ⁢                                                                                                                                          ⁢                                  12                                                                                                                                                                    )                                                                              }                                            ⁢                                                          ⁢                                                          ∴                              I                ⁢                                                                  ⁢                2                                      =                                          Vt                                  R                  ⁢                                                                          ⁢                  11                                            ⁢                              ln                ⁡                                  (                                                            I                      ⁢                                                                                          ⁢                                              1                        ·                        I                                            ⁢                                                                                          ⁢                                              012                        ·                                                                              W                            ⁢                                                                                                                  ⁢                            12                                                                                L                            ⁢                                                                                                                  ⁢                            12                                                                                                                                      I                      ⁢                                                                                          ⁢                                              2                        ·                        I                                            ⁢                                                                                          ⁢                                              011                        ·                                                                              W                            ⁢                                                                                                                  ⁢                            11                                                                                L                            ⁢                                                                                                                  ⁢                            11                                                                                                                                )                                                                                        (        4        )            
Furthermore, for simplifying of circuit analysis, let us consider a case where each of the transistors M13 to M17 operates in a saturation region, and influences by the body effect and the early effect are negligible. According to Japanese Patent Publication JP-2001-142552, W13/L13=W14/L14=W15/L15 and W16/L16=W17/L17. In this case, the following equations (5) and (6) can be obtained. Here, let VD11 denote a forward voltage of the PN junction diode D11.I1=I2=I3=I4  (5)V3=VD11+I3×R12=I4×R13  (6)
By substituting the equations (4) and (5) into the equation (6), we obtain the following equation (7).
                              I          ⁢                                          ⁢          4                =                                                            1                                  R                  ⁢                                                                          ⁢                  13                                            ·                              (                                                      VD                    ⁢                                                                                  ⁢                    11                                    +                                      I                    ⁢                                                                                  ⁢                                          3                      ·                      R                                        ⁢                                                                                  ⁢                    12                                                  )                                      ⁢                                                  ∴                          I              ⁢                                                          ⁢              4                                =                                    1                              R                ⁢                                                                  ⁢                13                                      ·                          {                                                VD                  ⁢                                                                          ⁢                  11                                +                                  Vt                  ·                                                            R                      ⁢                                                                                          ⁢                      12                                                              R                      ⁢                                                                                          ⁢                      11                                                        ·                                      ln                    ⁡                                          (                                                                        I                          ⁢                                                                                                          ⁢                                                      012                            ·                                                                                          W                                ⁢                                                                                                                                  ⁢                                12                                                                                            L                                ⁢                                                                                                                                  ⁢                                12                                                                                                                                                              I                          ⁢                                                                                                          ⁢                                                      011                            ·                                                                                          W                                ⁢                                                                                                                                  ⁢                                11                                                                                            L                                ⁢                                                                                                                                  ⁢                                11                                                                                                                                                        )                                                                                  }                                                          (        7        )            
Next, temperature dependence of the output current I4 in the case of the reference current generating circuit X1 is considered. For simplifying of circuit analysis, let us consider a case where resistance values of the resistors R11 to R13 have no temperature dependence. Since the N-channel MOS transistors M11 and M12 have the same characteristics, temperature characteristics of the respective drain currents I011 and I012 are the same, and therefore no temperature characteristic appears in a parameter “I012/I011”. Thus, in the equation (7), only the forward voltage VD11 and thermal voltage Vt have temperature characteristics. By differentiate both sides of the equation (7) with respect to absolute temperature T, the following equation (8) can be obtained.
                              ∴                                                    ∂                I                            ⁢                                                          ⁢              4                                      ∂              T                                      =                              1                          R              ⁢                                                          ⁢              13                                ·                      {                                                                                ∂                    VD                                    ⁢                                                                          ⁢                  11                                                  ∂                  T                                            +                                                k                  q                                ·                                                      R                    ⁢                                                                                  ⁢                    12                                                        R                    ⁢                                                                                  ⁢                    11                                                  ·                                  ln                  ⁡                                      (                                                                  I                        ⁢                                                                                                  ⁢                                                  012                          ·                                                                                    W                              ⁢                                                                                                                          ⁢                              12                                                                                      L                              ⁢                                                                                                                          ⁢                              12                                                                                                                                                  I                        ⁢                                                                                                  ⁢                                                  011                          ·                                                                                    W                              ⁢                                                                                                                          ⁢                              11                                                                                      L                              ⁢                                                                                                                          ⁢                              11                                                                                                                                            )                                                                        }                                              (        8        )            
Typically, the temperature dependences of the thermal voltage Vt and the forward voltage of the PN junction diode at an absolute temperature T=300 [K] (=27 degrees centigrade) are given as follows.
                                          ∂            VD                                ∂            T                          ≈                  -                      2            ⁢                                                  [                          m              ⁢                                                          ⁢              V              ⁢                              /                            ⁢              K                        ]                                              (        9        )                                          k          q                ≈                              1.38            ·                          10                              -                23                                                          1.60            ·                          10                              -                19                                                    ≈                  0.086          ⁢                                          [                      m            ⁢                                                  ⁢            V            ⁢                          /                        ⁢            K                    ]                                    (        10        )            
Therefore, a condition required for achieving the output current I4 having substantially no temperature dependence can be expressed by the following equation (11), which is obtained by substituting the equations (9) and (10) into the equation (8).
                    0        =                                            1                              R                ⁢                                                                  ⁢                13                                      ⁢                          {                                                                    -                    2                                    ·                                      10                                          -                      3                                                                      +                                  0.086                  ·                                      10                                          -                      3                                                        ·                                                            R                      ⁢                                                                                          ⁢                      12                                                              R                      ⁢                                                                                          ⁢                      11                                                        ·                                      ln                    ⁡                                          (                                                                        I                          ⁢                                                                                                          ⁢                                                      012                            ·                                                                                          W                                ⁢                                                                                                                                  ⁢                                12                                                                                            L                                ⁢                                                                                                                                  ⁢                                12                                                                                                                                                              I                          ⁢                                                                                                          ⁢                                                      011                            ·                                                                                          W                                ⁢                                                                                                                                  ⁢                                11                                                            L11                                                                                                                          )                                                                                  }                                ⁢                                          ∴                                                                      R                  ⁢                                                                          ⁢                  12                                                  R                  ⁢                                                                          ⁢                  11                                            ·                              ln                ⁡                                  (                                                            I                      ⁢                                                                                          ⁢                                              012                        ·                                                                              W                            ⁢                                                                                                                  ⁢                            12                                                                                L                            ⁢                                                                                                                  ⁢                            12                                                                                                                                      I                      ⁢                                                                                          ⁢                                              011                        ·                                                                              W                            ⁢                                                                                                                  ⁢                            11                                                                                L                            ⁢                                                                                                                  ⁢                            11                                                                                                                                )                                                      ≈            23.26                                              (        11        )            
However, the PN junction diode is an essential component in the reference current generating circuit X1 shown in FIG. 1. Meanwhile, a CMOSFET process is currently the most popular LSI process. The PN junction diode is not required for constituting only digital circuit. Moreover, the PN junction diode is not needed except for a partial exception (e.g. band gap reference circuit) in order to constituting an analog circuit by the CMOSFET process. In these circumstances, the PN junction diode is an additional element. In order to implement such an additional element, a time and costs of development increase because particular process for fabricating the additional element is needed. Moreover, the particular processes cause increase in costs of manufacturing a product. That is, the reference current generating circuit that uses the PN junction diode causes increase in a time and costs.